To me there are two cases (and I could be wrong I'm only recently reading up on Category Theory and I'm not nearly as versed as I should be in PL theory). One for generics whether you generate different copies for each type (monomorphization I believe?) and other cases where that doesn't necessarily make sense, although maybe you could just use generics to handle the problem in question. Hm.
I have to say I'm glad I started this thread because your reply and others have given me a lot to chew on.